Nuprl Lemma : prime-product-injection
Inj(bag(Prime);ℕ+;λb.Π(b))
Proof
Definitions occuring in Statement :
Prime: Prime,
int-bag-product: Π(b),
bag: bag(T),
inject: Inj(A;B;f),
nat_plus: ℕ+,
lambda: λx.A[x]
Definitions unfolded in proof :
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
Prime: Prime,
int_upper: {i...},
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
equal_wf,
nat_plus_wf,
int-bag-product_wf,
subtype_rel_bag,
Prime_wf,
bag-product-primes,
less_than_wf,
bag_wf,
factors_wf,
squash_wf,
true_wf,
factors-prime-product,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
hypothesisEquality,
applyEquality,
intEquality,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
because_Cache,
dependent_functionElimination,
natural_numberEquality,
applyLambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
Inj(bag(Prime);\mBbbN{}\msupplus{};\mlambda{}b.\mPi{}(b))
Date html generated:
2018_05_21-PM-07_23_04
Last ObjectModification:
2017_07_26-PM-05_06_07
Theory : general
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