Nuprl Lemma : play-truncate-trivial
∀[g:SimpleGame]. ∀[n:ℕ]. ∀[s:win2strat(g;n)]. ∀[f:strat2play(g;n;s)]. ∀[k:ℤ].
play-truncate(f;k) ~ f supposing k = ||f|| ∈ ℤ
Proof
Definitions occuring in Statement :
strat2play: strat2play(g;n;s),
win2strat: win2strat(g;n),
play-truncate: play-truncate(f;m),
play-len: ||moves||,
simple-game: SimpleGame,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
sq_type: SQType(T),
pi1: fst(t),
seq-len: ||s||,
seq-truncate: seq-truncate(s;n),
play-len: ||moves||,
play-truncate: play-truncate(f;m),
sequence: sequence(T),
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
nat: ℕ,
guard: {T},
subtype_rel: A ⊆r B,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtype_base_sq,
simple-game_wf,
nat_wf,
win2strat_wf,
strat2play_wf,
play-len_wf,
int_subtype_base,
equal-wf-base-T,
equal_wf,
seq-len_wf,
le_wf,
sg-pos_wf,
sequence_wf,
strat2play_subtype
Rules used in proof :
independent_isectElimination,
cumulativity,
instantiate,
productElimination,
isect_memberEquality,
intEquality,
sqequalAxiom,
independent_functionElimination,
dependent_functionElimination,
lambdaFormation,
because_Cache,
natural_numberEquality,
multiplyEquality,
addEquality,
setEquality,
rename,
setElimination,
lambdaEquality,
equalitySymmetry,
equalityTransitivity,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
thin,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:win2strat(g;n)]. \mforall{}[f:strat2play(g;n;s)]. \mforall{}[k:\mBbbZ{}].
play-truncate(f;k) \msim{} f supposing k = ||f||
Date html generated:
2018_07_25-PM-01_32_37
Last ObjectModification:
2018_06_27-PM-08_22_05
Theory : co-recursion
Home
Index