Nuprl Lemma : sg-change-init_wf
∀[g:SimpleGame]. ∀[j:Pos(g)]. (g@j ∈ SimpleGame)
Proof
Definitions occuring in Statement :
sg-change-init: g@j,
sg-pos: Pos(g),
simple-game: SimpleGame,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
pi1: fst(t),
sg-pos: Pos(g),
spreadn: spread4,
simple-game: SimpleGame,
sg-change-init: g@j,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
simple-game_wf,
set_wf,
subtype_rel_self,
subtype_rel_dep_function,
sg-pos_wf,
subtype_rel-equal,
sg-reachable_self,
sg-reachable_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaFormation,
rename,
setElimination,
lambdaEquality,
instantiate,
dependent_set_memberEquality,
independent_isectElimination,
dependent_functionElimination,
hypothesis,
because_Cache,
applyEquality,
universeEquality,
functionEquality,
cumulativity,
productEquality,
independent_pairEquality,
isectElimination,
extract_by_obid,
hypothesisEquality,
setEquality,
dependent_pairEquality,
thin,
productElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[j:Pos(g)]. (g@j \mmember{} SimpleGame)
Date html generated:
2018_07_25-PM-01_35_01
Last ObjectModification:
2018_06_20-PM-09_29_35
Theory : co-recursion
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