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 :
uall: ∀[x:A]. B[x],
sg-change-init: g@j,
member: t ∈ T,
simple-game: SimpleGame,
spreadn: spread4,
sg-pos: Pos(g),
pi1: fst(t),
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
istype: istype(T)
Lemmas referenced :
sg-pos_wf,
simple-game_wf,
sg-reachable_wf,
sg-reachable_self,
subtype_rel-equal,
subtype_rel_dep_function,
subtype_rel_universe1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
Error :universeIsType,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
productElimination,
sqequalRule,
Error :dependent_pairEquality_alt,
setEquality,
applyEquality,
because_Cache,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_isectElimination,
Error :dependent_set_memberEquality_alt,
instantiate,
cumulativity,
Error :lambdaEquality_alt,
functionEquality,
universeEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
setElimination,
rename,
Error :setIsType,
Error :productIsType,
Error :functionIsType
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[j:Pos(g)]. (g@j \mmember{} SimpleGame)
Date html generated:
2019_06_20-PM-00_54_06
Last ObjectModification:
2019_01_02-PM-01_32_23
Theory : co-recursion-2
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