Nuprl Rule : dependent_pairEquality
This rule proved as lemma rule_pair_equality_true in file rules/rules_product.v
at https://github.com/vrahli/NuprlInCoq
H ⊢ <a1, b1> = <a2, b2> ∈ (x:A × B)
BY dependent_pairEquality !parameter{i:l} y ()
H ⊢ a1 = a2 ∈ A
H ⊢ b1 = b2 ∈ B[a1/x]
H y:A ⊢ B[y/x] = B[y/x] ∈ Type
Definitions occuring in rule :
product: x:A × B[x],
pair: <a, b>,
equal: s = t ∈ T,
universe: Type,
axiom: Ax
Latex:
H \mvdash{} <a1, b1> = <a2, b2>
BY dependent\_pairEquality !parameter\{i:l\} y ()
H \mvdash{} a1 = a2
H \mvdash{} b1 = b2
H y:A \mvdash{} B[y/x] = B[y/x]
Date html generated:
2019_06_20-PM-04_11_57
Last ObjectModification:
2016_07_08-PM-03_49_01
Theory : rules
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