Nuprl Lemma : UallTest1
∀F:∀[T:Type]. (T ⟶ T). ∀S:Type. ∀s:S. ((F s) = s ∈ S)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
squash: ↓T
Lemmas referenced :
set_wf,
uall_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
hypothesisEquality,
universeEquality,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
cumulativity,
functionEquality,
applyEquality,
setEquality,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
dependent_functionElimination,
dependent_set_memberEquality,
setElimination,
rename,
imageMemberEquality,
baseClosed,
introduction,
imageElimination
Latex:
\mforall{}F:\mforall{}[T:Type]. (T {}\mrightarrow{} T). \mforall{}S:Type. \mforall{}s:S. ((F s) = s)
Date html generated:
2016_05_16-AM-09_05_03
Last ObjectModification:
2016_01_17-AM-09_41_27
Theory : C-semantics
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