Nuprl Lemma : page55
∀[U:Type]. ∀[P,Q:U ⟶ ℙ]. ((∀x:U. (P[x] ⇒ Q[x])) ⇒ (∀x:U. P[x]) ⇒ (∀x:U. Q[x]))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
because_Cache,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[U:Type]. \mforall{}[P,Q:U {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:U. (P[x] {}\mRightarrow{} Q[x])) {}\mRightarrow{} (\mforall{}x:U. P[x]) {}\mRightarrow{} (\mforall{}x:U. Q[x]))
Date html generated:
2016_05_15-PM-07_42_03
Last ObjectModification:
2015_12_27-AM-11_13_36
Theory : general
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