Nuprl Lemma : comb_for_pi1_wf
λA,B,p,z. (fst(p)) ∈ A:Type ⟶ B:(A ⟶ Type) ⟶ p:(a:A × B[a]) ⟶ (↓True) ⟶ A
Proof
Definitions occuring in Statement :
so_apply: x[s],
pi1: fst(t),
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
pi1_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
Error :productIsType,
applyEquality,
Error :functionIsType,
Error :inhabitedIsType,
universeEquality
Latex:
\mlambda{}A,B,p,z. (fst(p)) \mmember{} A:Type {}\mrightarrow{} B:(A {}\mrightarrow{} Type) {}\mrightarrow{} p:(a:A \mtimes{} B[a]) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} A
Date html generated:
2019_06_20-AM-11_18_19
Last ObjectModification:
2018_09_27-PM-05_34_15
Theory : core_2
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